Answer:
7.5
Explanation:
Given the following:
[tex]\begin{gathered} Z-\text{Score}=-2.4 \\ \text{Mean,}\mu=54 \\ X-\text{Value}=36 \end{gathered}[/tex]Substitute these into the formula for Z-Score:
[tex]Z-\text{Score}=\frac{X-\mu}{\sigma}\text{ where }\sigma=\text{standard deviation}[/tex]This gives:
[tex]\begin{gathered} -2.4=\frac{36-54}{\sigma} \\ -2.4=\frac{-18}{\sigma} \\ -2.4\sigma=-18 \\ \sigma=\frac{-18}{-2.4} \\ \sigma=7.5 \end{gathered}[/tex]The standard deviation is 7.5
